Use long division to convert 2/9 to a decimal. Your approximation should have one decimal place simplifed

Answer 1

To convert $\frac{2}{9}$ to a decimal using long division, we can follow these steps:

1. Set up the long division of 2 by 9. Since 2 is less than 9, we start by adding a decimal point and zeros (making it 2.000...).

2. Divide 2.0 by 9. Since 9 can’t go into 2, we look at 20 (after putting a decimal point):

   • 9 goes into 20 two times (because $9\times 2=18$).
   • Write 2 above the line.

3. Subtract 18 from 20: $$20-18=2$$

4. Bring down the next 0 (to make it 20 again):

   • Again, 9 goes into 20 two times (another $9\times 2=18$).
   • Write another 2 above the line.

5. Subtract 18 from 20 again: $$20-18=2$$

6. This process will repeat indefinitely, yielding the digits 222..., which goes on forever.

Thus, $\frac{2}{9}=0.222...$

To simplify $0.222...$ to one decimal place, we round it. Since the second decimal place (2) is less than 5, we round down.

Therefore, the value of $\frac{2}{9}$ rounded to one decimal place is: $$\boxed{{\displaystyle 0.2}}$$